Question

The length of the room is 2½ times the breadth. The perimeter of the room is 70 m. What are the length and breadth of the room.

Answer 1

Length = 25 cm

Breadth = 10 cm

Explanation:

Let breadth of the room be 'x'

Let length of the room be '
`2 (1)/(2) x = (5)/(2) = 2.5 \: x`'

Perimeter ( P ) = 70 cm

Now, let's find the breadth of the room 'x '

Perimeter of rectangle =
`2(l + b)`

plug the values

`70 = 2(2.5x + x)`

Collect the like terms

`70 = 2 * 3.5x`

Calculate the product

`70 = 7x`

Swap the sides of the equation

`7x = 70`

Divide both sides of the equation by 7

`(7x)/(7) = (70)/(7)`

Calculate

`x = 10 \: cm`

Breadth = 10 cm

Now, Let's find the length of the room ' 2.5x '

Length of the room =
`2.5x`

Plug the value of X

`= 2.5 * 10`

Calculate the product

`= 25 \: cm`

Thus , The length and breadth of the room is 25 cm and 10 cm respectively.

Hope this helps..

Best regards!!

Answer 2

According to the question

Let breadth be x

So length = 5/2. X

Now perimeter of rectangle = 2(l+b)

.

so

70 = 2 × ( X + 5/2 X)

35 = 7x/2

x = 35 × 2/7

x = 10

So breadth = 10m

length = 5/2 × 10 = 25m